This study consists of two parts, Part I and Part II. The purpose of Part I of the study is to assess the efficacy and safety of verubecestat (MK-8931) compared with placebo administered for 78 weeks in the treatment of Alzheimer's Disease (AD). The primary study hypotheses for Part I are that at least one verubecestat dose is superior to placebo at 78 weeks of treatment with respect to change from Baseline in Alzheimer's Disease Assessment Scale Cognitive Subscale (ADAS-Cog) score and that at least one verubecestat dose is superior to placebo at 78 weeks of treatment with respect to change from Baseline in Alzheimer's Disease Cooperative Study Activities of Daily Living Inventory (ADCS-ADL) score. The first approximately 400 participants entering Part I of the study are identified as the Safety Cohort. Participants who complete Part I of the study may choose to participate in Part II, which is a long term double-blind extension to assess efficacy and safety of verubecestat administered for up to an additional 260 weeks.